Atkins had to pay Florida based Moss £2.6m to take on the firm and its 50 staff.
Peter Brown reported an operating loss of £6.5m, on revenue of £24.4m, in the year to 31 March 2013.
Atkins expects to report a loss on disposal of approximately £3.0m in respect of the transaction.
Prof Dr Uwe Krueger, Atkins chief executive officer, said: “The disposal of our Peter Brown business is another step in the implementation of our strategy, which includes the optimisation of our portfolio of businesses.
“We believe Moss is a more appropriate company to take this business forward and this will allow our North American management team to focus on growing our core engineering consultancy business in the region.”